Abstract
An asymptotic theory for nonlinear analysis of multilayered anisotropic plates is developed on the basis of three-dimensional nonlinear elasticity without making a priori assumptions or omitting any nonlinear terms in the formulation. The laminated plate is regarded as an anisotropic heterogeneous plate with material properties varying in the thickness direction. Reformulation and nondimensionalization of the 3D equations of nonlinear elasticity reveal that the analysis can be carried out by means of asymptotic expansion and successive integration. It is shown that the von Karman nonlinear theory of laminated plates arises naturally as the first-order approximation to the 3D theory. Higher-order corrections can be determined systematically. In the formulation the boundary conditions on the top and bottom surfaces of the plate are satisfied and appropriate edge conditions associated with each level are derived. The theory accounts for the nonlinear effects in an adaptive and hierarchic way. There is no need to treat the system layer by layer or to consider the interfacial continuity conditions in particular.
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